138 research outputs found
Moduli Webs and Superpotentials for Five-Branes
We investigate the one-parameter Calabi-Yau models and identify families of
D5-branes which are associated to lines embedded in these manifolds. The moduli
spaces are given by sets of Riemann curves, which form a web whose intersection
points are described by permutation branes. We arrive at a geometric
interpretation for bulk-boundary correlators as holomorphic differentials on
the moduli space and use this to compute effective open-closed superpotentials
to all orders in the open string couplings. The fixed points of D5-brane moduli
under bulk deformations are determined.Comment: 41 pages, 1 figur
D-brane superpotentials and RG flows on the quintic
The behaviour of D2-branes on the quintic under complex structure
deformations is analysed by combining Landau-Ginzburg techniques with methods
from conformal field theory. It is shown that the boundary renormalisation
group flow induced by the bulk deformations is realised as a gradient flow of
the effective space time superpotential which is calculated explicitly to all
orders in the boundary coupling constant.Comment: 24 pages, 1 figure, v2:Typo in (3.14) correcte
Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds
We investigate the dynamics of space-time filling five-branes wrapped on
curves in heterotic and orientifold Calabi-Yau compactifications. We first
study the leading N=1 scalar potential on the infinite deformation space of the
brane-curve around a supersymmetric configuration. The higher order potential
is also determined by a brane superpotential which we compute for a subset of
light deformations. We argue that these deformations map to new complex
structure deformations of a non-Calabi-Yau manifold which is obtained by
blowing up the brane-curve into a four-cycle and by replacing the brane by
background fluxes. This translates the original brane-bulk system into a
unifying geometrical formulation. Using this blow-up geometry we compute the
complete set of open-closed Picard-Fuchs differential equations and identify
the brane superpotential at special points in the field space for five-branes
in toric Calabi-Yau hypersurfaces. This has an interpretation in open mirror
symmetry and enables us to list compact disk instanton invariants. As a first
step towards promoting the blow-up geometry to a supersymmetric heterotic
background we propose a non-Kaehler SU(3) structure and an identification of
the three-form flux.Comment: 95 pages, 4 figures; v2: Minor corrections, references update
Five-Brane Superpotentials and Heterotic/F-theory Duality
Under heterotic/F-theory duality it was argued that a wide class of heterotic
five-branes is mapped into the geometry of an F-theory compactification
manifold. In four-dimensional compactifications this identifies a five-brane
wrapped on a curve in the base of an elliptically fibered Calabi-Yau threefold
with a specific F-theory Calabi-Yau fourfold containing the blow-up of the
five-brane curve. We argue that this duality can be reformulated by first
constructing a non-Calabi-Yau heterotic threefold by blowing up the curve of
the five-brane into a divisor with five-brane flux. Employing
heterotic/F-theory duality this leads us to the construction of a Calabi-Yau
fourfold and four-form flux. Moreover, we obtain an explicit map between the
five-brane superpotential and an F-theory flux superpotential. The map of the
open-closed deformation problem of a five-brane in a compact Calabi-Yau
threefold into a deformation problem of complex structures on a dual Calabi-Yau
fourfold with four-form flux provides a powerful tool to explicitly compute the
five-brane superpotential.Comment: 43 pages, v2: minor correction
The Physics of the Colloidal Glass Transition
As one increases the concentration of a colloidal suspension, the system
exhibits a dramatic increase in viscosity. Structurally, the system resembles a
liquid, yet motions within the suspension are slow enough that it can be
considered essentially frozen. This kinetic arrest is the colloidal glass
transition. For several decades, colloids have served as a valuable model
system for understanding the glass transition in molecular systems. The spatial
and temporal scales involved allow these systems to be studied by a wide
variety of experimental techniques. The focus of this review is the current
state of understanding of the colloidal glass transition. A brief introduction
is given to important experimental techniques used to study the glass
transition in colloids. We describe features of colloidal systems near and in
glassy states, including tremendous increases in viscosity and relaxation
times, dynamical heterogeneity, and ageing, among others. We also compare and
contrast the glass transition in colloids to that in molecular liquids. Other
glassy systems are briefly discussed, as well as recently developed synthesis
techniques that will keep these systems rich with interesting physics for years
to come.Comment: 56 pages, 18 figures, Revie
Algorithmic deformation of matrix factorisations
Branes and defects in topological Landau-Ginzburg models are described by
matrix factorisations. We revisit the problem of deforming them and discuss
various deformation methods as well as their relations. We have implemented
these algorithms and apply them to several examples. Apart from explicit
results in concrete cases, this leads to a novel way to generate new matrix
factorisations via nilpotent substitutions, and to criteria whether boundary
obstructions can be lifted by bulk deformations.Comment: 30 page
Mirror Symmetry for Toric Branes on Compact Hypersurfaces
We use toric geometry to study open string mirror symmetry on compact
Calabi-Yau manifolds. For a mirror pair of toric branes on a mirror pair of
toric hypersurfaces we derive a canonical hypergeometric system of differential
equations, whose solutions determine the open/closed string mirror maps and the
partition functions for spheres and discs. We define a linear sigma model for
the brane geometry and describe a correspondence between dual toric polyhedra
and toric brane geometries. The method is applied to study examples with
obstructed and classically unobstructed brane moduli at various points in the
deformation space. Computing the instanton expansion at large volume in the
flat coordinates on the open/closed deformation space we obtain predictions for
enumerative invariants.Comment: 36 pages, references adde
Quantitative imaging of concentrated suspensions under flow
We review recent advances in imaging the flow of concentrated suspensions,
focussing on the use of confocal microscopy to obtain time-resolved information
on the single-particle level in these systems. After motivating the need for
quantitative (confocal) imaging in suspension rheology, we briefly describe the
particles, sample environments, microscopy tools and analysis algorithms needed
to perform this kind of experiments. The second part of the review focusses on
microscopic aspects of the flow of concentrated model hard-sphere-like
suspensions, and the relation to non-linear rheological phenomena such as
yielding, shear localization, wall slip and shear-induced ordering. Both
Brownian and non-Brownian systems will be described. We show how quantitative
imaging can improve our understanding of the connection between microscopic
dynamics and bulk flow.Comment: Review on imaging hard-sphere suspensions, incl summary of
methodology. Submitted for special volume 'High Solid Dispersions' ed. M.
Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009);
22 pages, 16 fig
Flat Connections in Open String Mirror Symmetry
We study a flat connection defined on the open-closed deformation space of
open string mirror symmetry for type II compactifications on Calabi-Yau
threefolds with D-branes. We use flatness and integrability conditions to
define distinguished flat coordinates and the superpotential function at an
arbitrary point in the open-closed deformation space. Integrability conditions
are given for concrete deformation spaces with several closed and open string
deformations. We study explicit examples for expansions around different limit
points, including orbifold Gromov-Witten invariants, and brane configurations
with several brane moduli. In particular, the latter case covers stacks of
parallel branes with non-Abelian symmetry.Comment: 38 pages, 1 figure, v2: references adde
Computing Brane and Flux Superpotentials in F-theory Compactifications
In four-dimensional F-theory compactifications with N=1 supersymmetry the
fields describing the dynamics of space-time filling 7-branes are part of the
complex structure moduli space of the internal Calabi-Yau fourfold. We
explicitly compute the flux superpotential in F-theory depending on all complex
structure moduli, including the 7-brane deformations and the field
corresponding to the dilaton-axion. Since fluxes on the 7-branes induce 5-brane
charge, a local limit allows to effectively match the F-theory results to a
D5-brane in a non-compact Calabi-Yau threefold with threeform fluxes. We
analyze the classical and instanton contributions to the F-theory
superpotential using mirror symmetry for Calabi-Yau fourfolds. The F-theory
compactifications under consideration also admit heterotic dual descriptions
and we discuss the identification of the moduli in this non-perturbative
duality.Comment: 75 pages, 1 figure; typos corrected, references adde
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